The format evades simple definition: part-gig, part-interactive theatre, part-political rally. It's also not easy to find. The performance takes place in a secret location, which audience members are directed to via email. They are also instructed to bring a book they wish to exchange, and to wear something red.

Giangiacomo Feltrinelli (left) with director David Lean.

The venue (about which I can say no more than that it's a short walk from Cardiff station) would be indistinguishable from any other industrial unit, were it not for the thumpingly loud techno coming through the walls. Inside, there is a bare concrete floor and an assortment of office equipment, all of it scaled up to an enormous size. It's as if you've been given an Alice in Wonderland potion in a stationery warehouse.

Rhys, wearing a shaggy beard and woolly hat, is an imposing figure – somewhat diminished by the 20ft-high filing cabinet next to him. "It is a bit strange," he admits. "There are two things rock musicians are really supposed to avoid: making concept albums and dabbling with theatre. But here I am doing both."

There's a reasonable chance the project will not end up a celebrated fiasco such as Rick Wakeman's King Arthur on Ice. The associated artists have a reassuring pedigree: writer Tim Price was responsible for National Theatre Wales's acclaimed touring show The Radicalisation of Bradley Manning; director Wils Wilson specialises in cross-genre, site-specific happenings; the choreography comes from Frantic Assembly's Scott Graham. After Cardiff, the show will appear at festivals throughout the summer.

How did the theatre element come about? "It all started with the DeLorean project," Rhys says in his quiet, methodical manner (he is first and foremost Welsh-speaking). This was a 2008 album inspired by the American motoring mogul, again made with Boom Bip (the pair perform as the electronic duo Neon Neon). "We were touring that album, and the shows gradually became more theatrical," Rhys says. "Har Mar Superstar [the musician and performance artist] came on board to play John DeLorean. A dance group told us they had worked out some moves, so they joined in as well. But it was all very ad hoc – at the end we said, 'Next time it would be nice to do this properly.'"

All that remained was to find another suitably controversial figure. Rhys realised he had his man when a friend recommended a biography written by Feltrinelli's son. It is quite a narrative: born into a privileged family, Feltrinelli became passionately interested in workers' rights. He was the first person to publish Boris Pasternak's Dr Zhivago, having smuggled the manuscript out of Russia. He went missing in Bolivia, endured interrogation by the CIA, and was photographed playing basketball with the Cuban revolutionary leader – an episode that inspired a track called Hoops With Fidel. Returning to Italy, he became involved in leftwing paramilitary activity. "It's quite hard to think of any British equivalent," Rhys says. "It would be like discovering Richard Branson was secretly running a terrorist organisation."

Feltrinelli playing basketball with Fidel Castro

The unexplained gaps in the publisher's career became a blank canvas to be filled with Boom Bip's oblique, synthpop soundscapes. "Feltrinelli idolised Castro," Boom Bip says. "His great dream was to establish a communist republic on the island of Sardinia. So what we've tried to do is imagine the kind of music that might have come out of Feltrinelli's Mediterranean Cuba, had it ever existed."

The publisher's death has never been adequately explained. Some suggest he was assassinated by the Italian authorities, rather than a victim of his own faulty timer. "Even in his own country, he name of Feltrinelli is mostly associated with bookstores, or leftwing extremism from a period in Italian history that people would rather forget," says Rhys. "But we looked through the family archives in Milan and there he is with Che Guevara, with Warhol, with Hemingway. He had this uncanny ability to keep cropping up at critical moments in 20th-century history – like a communist Forrest Gump."